Area calculations
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<p>The area of a triangle made up of three vertices A(x1,y1,z1), B(x2,y2,z2) and C(x3,y3,z3) can be represented <br>by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex. <br>For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:<br> | <p>The area of a triangle made up of three vertices A(x1,y1,z1), B(x2,y2,z2) and C(x3,y3,z3) can be represented <br>by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex. <br>For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:<br> | ||
Area of Triangle ABC = 1/2 ABS( AB x AC ) ; <br> | Area of Triangle ABC = 1/2 ABS( AB x AC ) ; <br> | ||
| - | AB = Vector from vertex A to vertex B <br> | + | AB = Vector from vertex A to vertex B. <br> |
AC = Vector from vertex A to vertex C. <br> | AC = Vector from vertex A to vertex C. <br> | ||
| + | ABS( X ) = function returns absolute value of X. <br> | ||
</p> | </p> | ||
== Area of Polygonal Surface == | == Area of Polygonal Surface == | ||
<p>A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon <br>can be approximated by sum of all triangle-areas it is made up of.</p> | <p>A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon <br>can be approximated by sum of all triangle-areas it is made up of.</p> | ||
Revision as of 08:32, 12 September 2005
Area of Triangle
The area of a triangle made up of three vertices A(x1,y1,z1), B(x2,y2,z2) and C(x3,y3,z3) can be represented
by the vector-cross-product of vectors along two sides of the triangle sharing a common vertex.
For the above mentioned triangle we have three sides as AB, BC and CA, the area of triangle is given by:
Area of Triangle ABC = 1/2 ABS( AB x AC ) ;
AB = Vector from vertex A to vertex B.
AC = Vector from vertex A to vertex C.
ABS( X ) = function returns absolute value of X.
Area of Polygonal Surface
A polygon can be divided into triangles sharing a common vertex of the polygon. The total area of the polygon
can be approximated by sum of all triangle-areas it is made up of.
